Determination of binary diffusion coefficients of gases using photothermal deflection technique

A photothermal deflection (PD) technique was applied to measure the binary diffusion coefficients of various gases (CO₂–N₂, CO₂–O₂, N₂–He, O₂–He, and CO₂–He). With an in-house-made Loschmidt diffusion cell, a transverse PD system was employed to measure the time-resolved PD signal associated with the variation of the thermal diffusivity and the temperature coefficient of the refractive index of the gas mixture during the diffusion. The concentration evolution of the gas mixture was deduced from the PD amplitude and phase signals based on our diffraction PD model and was processed using two mass-diffusion models explored in this work for both short- and long-time diffusions to find the diffusion coefficient. An optical fiber oxygen sensor was also used to measure the concentration changes of the mixtures with oxygen. Experimental results demonstrated that the binary diffusion coefficients precisely measured with the PD technique were in agreement with the literature values. Moreover, the PD technique can measure the diffusion coefficients of various gas mixtures with both short- and long-time diffusions. In contrast, the oxygen sensor is only suitable for the long-time diffusion measurements of the gas mixtures with oxygen. PACS 78.20.Nv; 51.20.+d     

Pulsed-Field-Gradient Measurements of Time-Dependent Gas Diffusion

Pulsed-field-gradient NMR techniques are demonstrated for measurements of time-dependent gas diffusion. The standard PGSE technique and variants, applied to a free gas mixture of thermally polarized xenon and O₂, are found to provide a reproducible measure of the xenon diffusion coefficient (5.71 × 10⁻⁶m²s⁻¹for 1 atm of pure xenon), in excellent agreement with previous, non-NMR measurements. The utility of pulsed-field-gradient NMR techniques is demonstrated by the first measurement of time-dependent (i.e., restricted) gas diffusion inside a porous medium (a random pack of glass beads), with results that agree well with theory. Two modified NMR pulse sequences derived from the PGSE technique (named the Pulsed Gradient Echo, or PGE, and the Pulsed Gradient Multiple Spin Echo, or PGMSE) are also applied to measurements of time dependent diffusion of laser polarized xenon gas, with results in good agreement with previous measurements on thermally polarized gas. The PGMSE technique is found to be superior to the PGE method, and to standard PGSE techniques and variants, for efficiently measuring laser polarized noble gas diffusion over a wide range of diffusion times.     

Transient-state method for coupled evaluation of Soret and Fick coefficients,and related tortuosity factors,using free and porous packed thermodiffusion cells: Application to CuSO4 aqueous solution ( 0.25M)

The measurement of Soret coefficients in liquids is not easy and usually not very precise because the resulting concentration gradient is small and moreover can be perturbed by undesired convection currents. In order to suppress, or to drastically reduce these convection currents, the use of a porous medium is sometimes suggested. The question arises as to whether the Soret coefficient is the same in free fluid and in porous medium. This is the aim of this paper. To this end, for a given liquid mixture, the time evolution of the vertical concentration gradient is experimentally measured in the same thermodiffusion cell filled first with the free liquid and next with a porous medium followed by saturation by the liquid mixture. Both the isothermal diffusion (Fick) coefficient and the Soret coefficient can be deduced, providing that a correct working equation is used. The proposed equation results from integration of the general mass conservation equation with realistic boundary conditions (zero mass flux at the boundaries) and some simplifying assumptions rendering this equation more tractable than the one proposed some decades ago by Bierlein (J.A. Bierlein, J. Chem. Phys. 23, 10 (1955)). The method is applied here to an electrolytic solution (CuSO4, 0.25 M) at a mean temperature of 37^°C. The Soret coefficients in free and porous medium (zircon microspheres in the range of 250- 315 ^. 10^-6m) may be considered to be equal ( S_T = 13.2±0.5 ^. 10^-3 K^-1) and the tortuosity factors for the packed medium are the same relative to thermodiffusion and Fick coefficients ( = 1.51±0.02).     

Application of the diffraction theory for photothermal deflection to measurements of thermophysical and mass-diffusion properties of gases

The application of recently developed diffraction theory for cw transverse photothermal deflection spectroscopy (normal deflection only) to the measurements of thermophysical and mass-diffusion properties of gases is presented. Compared with the traditional ray-optics theory, the diffraction theory has one more term in the phase signal. This term quantitatively exhibits the probe-beam size effect on the phase signal. Experimental results demonstrated that even if the ratio of the probe-beam radius to the thermal diffusion length of a deflecting medium was as low as about 0.22, the probe-beam size effect could not be ignored when measuring the distance between the probe beam and a solid sample using the phase signal. With the measured distance, the thermal diffusivity α_g and the temperature coefficient of the refractive index dn/dT of pure gases (O₂, N₂, and CO₂) and binary gas mixtures (CO₂-O₂ and CO₂-O₂) were precisely measured, resulting in good agreement with literature values. Furthermore the measured dn/dT values of the pure gases had one more significant figure than the literature ones. The concentration dependences of α_g and dn/dT were employed for the determination of mass-diffusion coefficients of CO₂-O₂ and CO₂-N₂, and the results were consistent with literature values.     

Theoretical investigations of rotational phenomena and dielectric properties in a nematic liquid crystal

The molecular dynamics (MD) simulation, based on a realistic atom-atom interaction potential, was performed on 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic phase. The rotational viscosity coefficients (RVCs) γ _i, (i = 1, 2) and the ratio of the RVCs λ = - γ ₂/γ ₁ were investigated. Furthermore, static and frequency-dependent dielectric constants and ε were calculated using parameters obtained from the MD simulation. Time correlation functions were computed and used to determine the rotational diffusion coefficient, D _⊥. The RVCs and λ were evaluated using the existing statistical-mechanical approach (SMA), based on a rotational diffusion model. The SMA rests on a model in which it is assumed that the reorientation of an individual molecule is a stochastic Brownian motion in a certain potential of mean torque. According to the SMA, γ _i are dependent on the orientational order and rotational diffusion coefficients. The former was characterized using: i) orientational distribution function (ODF), and ii) a set of order parameters, both derived from analyses of the MD trajectory. A reasonable agreement between the calculated and experimental values of γ _i and λ was obtained. Received 22 March 2000 and Received in final form 8 October 2000     

Determination of proton diffusion in solid electrolytes

Two electrochemical methods have been used to determine the proton diffusion in solid electrolytes. One is based on transient ionic current measurements and a reasonable physical model; the other one is a quick determination using steady-state transport. The results of proton diffusion coefficients of 10⁻⁶ and 10⁻⁵ cm²/s obtained for the α- and β-phases of Li₂SO₄, respectively, using these two methods are in a good agreement with published results. The methods turned out to be very useful for determining proton diffusion in solid electrolytes, especially when the electrolytes contain more than one type of the mobile ionic species and a low concentration of the protons. Paper presented at the 4th Euroconference on Solid State Ionics, Renvyle, Galway, Ireland, Sept. 13–19, 1997     

Investigation of electrochromic tungsten trioxide thin films prepared by the ILGAR method

An ion layer gas reaction dip coating process for the deposition of tungsten trioxide has been developed. Thin films of electrochromic tungsten trioxide with thicknesses of up to 150 nm were prepared. The films were found to be microcrystalline by X-ray diffraction analysis. The growth rate of the films was measured by profilometry. The chemical diffusion coefficient of lithium was investigated as a function of the concentration of lithium by the electrochemical galvanostatic intermittent titration technique. The chemical diffusion coefficient was found to increase slightly from 7×10⁻¹² to 3×10⁻¹ cm²/s, with x increasing from 0.2 to 0.8 in Li _x WO₃.     

Diffusion of sodium,potassium, calcium,manganese, and radon in tuff and clinoptilolite under leaching

Nuclear physics methods are used to determine the diffusion coefficients of Na, Ca, Mn, K, and ²²²Rn in clinoptilolite (Sokirnitsa occurrence, Ukraine) and in natural tuff (Yucca Mountain, Nevada, United States) and in tuff irradiated by γ-quanta (E _max = 23 MeV) to a dose of 10⁷ Gy at a leaching temperature of 37°C. The diffusion coefficients of sodium and potassium in clinoptilolite are found to differ considerably: 4 × 10⁻¹⁷ and 2 × 10⁻²⁰ m²/s, respectively. This indicates the influence of aquacomplexes on the cation transfer. The diffusion coefficient of radon in these materials is determined: in clinoptilolite it equals 2.5 × 10⁻¹² m²/s.     

Determination of parameters of Cu surface mass transport on sapphire from morphological changes of beaded films caused by evaporation

s , the surface diffusion coefficient, D_s ^′, and the surface reaction rate coefficient, β_s ^′, of Cu on alumina are determined in the temperature range 1048–1198 K. Measuring simultaneously the time dependence of the effective thickness, H_eff(t), the lateral shift of the boundary, y(t) of beaded films (BF) and using vapour pressure data we concluded that the process is controlled by surface reaction at the perimeters of beads. Supposing Arrhenius-type temperature dependence for D_s ^′, β_s ^′ and λ_s the activation energies and preexponential factors have been calculated. Received: 2 October 1996/Accepted: 27 November 1996     

Gas temperature measurements using widely tunable long-wavelength VCSEL

A method for gas temperature measurements with a widely tunable laser diode is presented. The method involves rapidly switching the laser frequency between two distantly spaced absorption lines chosen for optical thermometry. Direct absorption spectroscopy using a single-mode VCSEL was employed to probe the R10 and R22 lines of the 2ν₁+2ν₂ ⁰+ν₃ combination band of CO₂ near 6355.9 and 6363.7 cm^-1 sequentially. A specially designed 0.5-m cryogenic gas cell was filled with 10 mbar CO₂ at room temperature and cooled to 150 K with liquid N₂. The VCSEL was modulated with a 10-kHz ramp superimposed on a 1-kHz square waveform to scan two 0.04 cm^-1 intervals sequentially. The gas temperatures obtained with the VCSEL in the 150–300 K range are in a good agreement with those derived from gas pressure ratios. The maximum relative error of temperature measurements using the VCSEL was ± 3%. A compact VCSEL-based sensor can be developed for gas temperature and concentration measurements in the Martian atmosphere. The method proposed can be used for many applications including in situ monitoring of combustion processes. PACS 42.62.Fi; 42.55.Px; 39.30.+w     

Kinetics of the sorption of <Superscript>3</Superscript>He by C<Subscript>60</Subscript> fullerite. The quantum diffusion of <Superscript>3</Superscript>He and <Superscript>4</Superscript>He in fullerite

The kinetics of the sorption and subsequent desorption of gaseous ³He in a C₆₀ fullerite powder has been studied in the temperature range of 2–292 K. The temperature dependences of the diffusion coefficients of ³He and ⁴He impurities in fullerite have been plotted using the measured characteristic times of filling of octahedral and tetrahedral interstices, as well as previous data. These temperature dependences of the diffusion coefficients of ³He and ⁴He impurities in fullerite are qualitatively similar. A decrease in the temperature from 292 to 79 K is accompanied by a decrease in the diffusion coefficients, which corresponds to the dominance of the thermally activated diffusion of helium isotopes in fullerite. A further decrease in the temperature to 8–10 K leads to an increase in the diffusion coefficients by more than an order of magnitude. The diffusion coefficients of ³He and ⁴He are independent of the temperature below 8 K, indicating the tunnel character of the diffusion of helium in C₆₀ fullerite. The isotope effect is manifested in the difference between the absolute values of the diffusion coefficients of ³He and ⁴He atoms at the same temperatures.     

Preparation and characterization of a poled nanocrystal and polymer composite PbTiO3/PEKc film for electro-optic applications

Composite thin films of PbTiO₃ nanocrystals and high-transparency PEKc polymer for applications in electro-optical devices were prepared using the spin coating technique. The size of the PbTiO₃ nanocrystals was estimated to be 30–40 nm using a transmission electron microscope. The transmission technique, a simple method for measuring the electro-optic coefficients of poled composite polymer films was developed. The electro-optic coefficient γ₃₃ of poled PbTiO₃/PEKc composite polymer films was measured to be 18.34 pm  V^-1 at 633 nm under room temperature. The index at 633 nm and the dielectric constant at 100 kHz under room temperature were determined to be 1.65248 and 7.32, respectively. The figure of merit F₂=n⁷γ²/ε was estimated to be 1546, showing very good electro-optical properties. Received: 5 February 2002 / Accepted: 12 March 2002 / Published online: 19 July 2002 RID="*" ID="*"Corresponding author. Fax: +852/2788-7791, E-mail: eeytc@cityu.edu.hk     

Positron investigations of free-volume elements in polymer gas-separation membranes

This work is a part of an investigation aimed at converting the positron method into a tool for quantitative investigations of microdefects in polymers. The number (10¹⁹ cm⁻³) and effective radii (0.2–2.8 nm) of elementary free volumes in polymer gas-separation membranes polytrimethyl silylpropine (PTMSP) and porous polyphenylene oxide (PPO 200 and 70 m²/g) are estimated on the basis of positron data. The calculations are facilitated by using the mutually complementary programs PATFIT and CONTIN as well as by the possibility of estimating the diffusion coefficients of positronium in PPO samples having different specific surface areas. Fiz. Tverd. Tela (St. Petersburg) 40, 164–167 (January 1998)     

High Temperature Diffusion of 6Li Adsorbed on a Ru(001) Single Crystal Surface as Seen by Pulse NMR

Diffusion measurements on lithium atoms adsorbed on a ruthenium single crystal were performed in the high temperature regime (1100–1200 K). Pulsed NMR techniques were utilized to produce and observe the decay of magnetization patterns from which the diffusion coefficient was extracted. The observed temperature dependence could be described by D = (10 ± 7) cm²/s · exp (−(0.46 ± 0.07) eV/kT). The extremely high diffusion coefficient and prefactor are understood by a gas like adsorbate behavior. The electric field gradient has been measured with ⁷Li: V _zz = −5.0 ± 0.1 10¹⁵ V/cm² with an inhomogeneity of less then 1% as judged by the width of the satellite transitions.     

Diffusion study of <Superscript>18</Superscript>O implanted into α-Ti using the nuclear resonance technique

The diffusion of ¹⁸O in α-Tiwas studied in the 623–873 K temperature range by using the ion implantation and nuclear resonance techniques. The measurements show that the diffusion coefficients follow an Arrhenius behavior with diffusion parameters D₀=(2±1)10^-7 m² s^-1 and Q=(±) 16950kJ/mol, values typical of interstitial diffusion mechanism. A comparison of the present and previous results is also done. PACS 66.30.Jt; 85.40.Ry     

Erbium incorporation in LiNbO3 by diffusion-doping

 The erbium incorporation into LiNbO₃ by diffusion doping is investigated in detail by means of Secondary Ion Mass Spectrometry, Secondary Neutral Mass Spectrometry, Rutherford Backscattering, Atomic Force Microscopy, X-ray Standing Wave technique and optical site-selective spectroscopy. The diffusion of erbium in LiNbO₃ can be described by Fick’s laws of diffusion with a concentration-independent diffusion coefficient. The diffusion constants and activation energies for Z-cut (X-cut) LiNbO₃ are 4.8×10^-5 cm²/s (12.0×10^-5 cm²/s) and 2.28 eV (2.44 eV), respectively. A limited solubility of erbium in LiNbO₃ has to be taken into account increasing exponentially with rising temperature. During the first step of diffusion an Er _x Nb _y -oxide layer is formed at the surface of the sample acting as diffusion reservoir. Erbium is incorporated into LiNbO₃ on vacant Li-sites slightly shifted from the original Li-position along the (-c)-direction. Site-selective spectroscopy found four distinguishable energetically different erbium centres at this lattice site resulting from locally different symmetries of the crystal field. Received: 21 March 1996 / Accepted: 12 August 1996     

Equalization of reflectance of parallel-polarized electromagnetic plane waves at normal and oblique incidence of interfaces between transparent media and its use for measurement of the dielectric constant

A new angle of incidence of significance, when considering the reflection of electromagnetic waves at interfaces between transparent media, is defined. At this angle, denoted by φ_e, the reflection coefficient of parallel-polarized radiation is equal in magnitude and opposite in sign to the reflection coefficient at normal incidence. No similar angle exists for the perpendicular polarization. If ε is the relative dielectric constant, i.e., the ratio of the dielectric constant of the medium of refraction to that of the medium of incidence, we find that tan φ_e=(ε²+ε)^1/2. Measurement of φ_e, by equalization of the absolute (intensity) reflectances at normal and oblique incidence, allows ε to be determined using the inverse relation ε=(tan²φ_e+1/4)^1/2−1/2.     

Diffusion study of <Superscript>15</Superscript>N implanted into α-Ti using the nuclear resonance technique

The diffusion of ¹⁵N in α-Ti was studied in the 673–1023 K temperature range by using the ion implantation and nuclear resonance techniques. The measurements show that the diffusion coefficients follow an Arrhenius behavior D(T)=D₀ ^-Q/RT, where D₀=(1.1±0.8)×10^-7 m² s^-1 and Q=(183±2) kJ/mol. A comparison with previous results is also given. PACS 66.30.Jt; 85.40.Ry     

Composition dependence of the ionic diffusion coefficients in yttria-stabilized zirconias

The diffusion coefficient of the O²⁻ ions in yttria-stabilized zirconia (1−x)ZrO₂·xYO_1.5 has been investigated as a function of the concentration of Y³⁺ ion over a range x = 0.131–0.261 by using quasielastic light scattering. The diffusion coefficients were deduced from the analysis of the temperature dependence of the scattering intensity at 3 GHz. It is concluded that the diffusion coefficient reaches its maximum value at x = 0.165. The composition dependence of the scattering intensity suggests that the concentration of the moving carrier decreases as the Y³⁺ content increases in spite of an increase of the oxygen vacancies.     

Influence of the noise driving force on the diffusion of copper in aluminium thin films

The diffusion of copper in thin polycrystalline aluminium films subjected to current stressing at 140 C was studied. Experimental aluminium stripes were doped with copper in a limited (source) region and the movement of copper away from this region was investigated by electron probe microanalyser. Samples were stressed both by dc and by superimposed dc and noise current. The dc density (5×10⁵ A/cm²) was equal to that of the effective (r.m.s.) value of superimposed current. The frequency range of the noise signal with the Gaussian distribution of amplitudes was 5 Hz to 20 kHz. Under the described conditions copper diffused due to the concentration gradient as well as the electromigration driving force. The diffusion coefficients of copper at both current stressings were obtained by fitting the measured concentration profiles to those calculated theoretically. The results yield that the diffusion becomes enhanced when the noise is applied. The values of thermal grain boundary-assisted diffusion coefficient obtained in six independent measurements with dc loading vary betweenD _Tb=8×10^–13 cm²/s and 25×10^–13 cm²/s. The corresponding values of total diffusion coefficient (i.e. the sum of the thermal and noise induced component) areD _b=(20÷83)×10^–13 cm²/s. The noise-induced enhancement of the diffusion was predicted theoretically. Thus, the present results confirm the previous theoretical calculations.The authors wish to thank Dr. V. Bezák for stimulating discussions.